Problem: Express your answer as a mixed number simplified to lowest terms. $17\dfrac{7}{15}-8\dfrac{7}{9} = {?}$
Solution: Find a common denominator for the fractions: $= {17\dfrac{21}{45}}-{8\dfrac{35}{45}}$ Convert ${17\dfrac{21}{45}}$ to ${16 + \dfrac{45}{45} + \dfrac{21}{45}}$ So the problem becomes: ${16\dfrac{66}{45}}-{8\dfrac{35}{45}}$ Separate the whole numbers from the fractional parts: $= {16} + {\dfrac{66}{45}} - {8} - {\dfrac{35}{45}}$ Bring the whole numbers together and the fractions together: $= {16} - {8} + {\dfrac{66}{45}} - {\dfrac{35}{45}}$ Subtract the whole numbers: $=8 + {\dfrac{66}{45}} - {\dfrac{35}{45}}$ Subtract the fractions: $= 8+\dfrac{31}{45}$ Combine the whole and fractional parts into a mixed number: $= 8\dfrac{31}{45}$